Ploidacot/Monocot - Revision history

FloraC: Text replacement - "[[Category:Ploidacot" to "[[Category:Ploidacots"

2026-01-06T09:43:21Z

Text replacement - "[[Category:Ploidacot" to "[[Category:Ploidacots"

← Older revision		Revision as of 09:43, 6 January 2026
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	[[Trienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.		[[Trienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.

	[[Category:~~Ploidacot~~\|Monocot]]		[[Category:Ploidacots\|Monocot]]

Xenllium at 22:07, 5 January 2026

2026-01-05T22:07:31Z

← Older revision		Revision as of 22:07, 5 January 2026
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	== Intervals and notation ==		== Intervals and notation ==
	Monocot is the only ploidacot to have an agreed-upon, fully unambiguous scheme for interval and note names, which can be found at [[~~Chain~~-of-fifths notation]].		Monocot is the only ploidacot to have an agreed-upon, fully unambiguous scheme for interval and note names, which can be found at [[chain-of-fifths notation]].

	{\| class="wikitable"		{\| class="wikitable"
Line 50:		Line 50:
	\| '''0'''		\| '''0'''
	\| '''C'''		\| '''C'''
	\| Perfect unison ~~/ Perfect octave~~		\| Perfect unison
	\|-		\|-
	\| 1		\| 1
	\| 498.05		\| 498.04
	\| F		\| F
	\| Perfect fourth		\| Perfect fourth
Line 63:		Line 63:
	\|-		\|-
	\| 3		\| 3
	\| 294.14		\| 294.13
	\| Eb		\| Eb
	\| Minor third		\| Minor third
Line 83:		Line 83:
	\|-		\|-
	\| 7		\| 7
	\| 1,086.32		\| 1,086.31
	\| Cb		\| Cb
	\| Diminished octave		\| Diminished octave
Line 113:		Line 113:
	[[Trienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.		[[Trienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.

	[[Category:Ploidacot]]		[[Category:Ploidacot\|Monocot]]

Xenllium: /* Temperament interpretations */

2026-01-04T01:58:19Z

Temperament interpretations

← Older revision		Revision as of 01:58, 4 January 2026
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	[[Trienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.		[[Trienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.

	~~{{Todo\| unify precision }}~~		[[Category:Ploidacot]]

VectorGraphics at 23:25, 25 October 2025

2025-10-25T23:25:44Z

← Older revision		Revision as of 23:25, 25 October 2025
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=1\|Pergen=[P8, P5]\|Forms=5, 7, 12\|Title=Monocot}}'''Monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth, and the period is a [[2/1]] octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale ([[5L 2s]]) and one of its chromatic children ([[5L 7s]] or [[7L 5s]]) (though there are exotempered exceptions such as [[mavila]] ([[2L 5s]]) and [[trienstonian]] ([[5L 3s]])) and as such they are very commonly used and are a well-explored category of temperaments.		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=1\|Pergen=[P8, P5]\|Forms=5, 7, 12\|Title=Monocot\|Wedgie=1}}'''Monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth, and the period is a [[2/1]] octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale ([[5L 2s]]) and one of its chromatic children ([[5L 7s]] or [[7L 5s]]) (though there are exotempered exceptions such as [[mavila]] ([[2L 5s]]) and [[trienstonian]] ([[5L 3s]])) and as such they are very commonly used and are a well-explored category of temperaments.

	== Intervals and notation ==		== Intervals and notation ==

ArrowHead294 at 15:44, 9 September 2025

2025-09-09T15:44:36Z

← Older revision		Revision as of 15:44, 9 September 2025
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=1\|Pergen=[P8, P5]\|Forms=5, 7, 12\|Title=Monocot}}'''Monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth, and the period is a [[2/1]] octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale ([[5L 2s]]) and one of its chromatic children ([[5L 7s]] or [[7L 5s]]) (though there are exotempered exceptions such as [[mavila]] ([[2L 5s]]) and [[trienstonian]] ([[5L 3s]])) and as such they are very commonly used and are a well-explored category of temperaments.		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=1\|Pergen=[P8, P5]\|Forms=5, 7, 12\|Title=Monocot}}'''Monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth, and the period is a [[2/1]] octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale ([[5L 2s]]) and one of its chromatic children ([[5L 7s]] or [[7L 5s]]) (though there are exotempered exceptions such as [[mavila]] ([[2L 5s]]) and [[trienstonian]] ([[5L 3s]])) and as such they are very commonly used and are a well-explored category of temperaments.

	== Intervals and notation ==		== Intervals and notation ==
	Monocot is the only ploidacot to have an agreed-upon, fully unambiguous scheme for interval and note names, which can be found at [[Chain-of-fifths notation]].		Monocot is the only ploidacot to have an agreed-upon, fully unambiguous scheme for interval and note names, which can be found at [[Chain-of-fifths notation]].

	{\| class="wikitable"		{\| class="wikitable"
	\|+Monocot intervals (assuming pure fifth and octave)		\|+ style="font-size: 105%;" \| Monocot intervals (assuming pure fifth and octave)
	!#		\|-
	!Steps		! #
	!Notation		! Steps
	!Name		! Notation
			! Name
	\|-		\|-
	\| -7		\| −7
	\|113.69		\| 113.69
	\|C#		\| C#
	\|Augmented unison		\| Augmented unison
	\|-		\|-
	\| -6		\| −6
	\|611.73		\| 611.73
	\|F#		\| F#
	\|Augmented fourth		\| Augmented fourth
	\|-		\|-
	\| -5		\| −5
	\|1,109.78		\| 1,109.78
	\|B		\| B
	\|Major seventh		\| Major seventh
	\|-		\|-
	\| -4		\| −4
	\|407.82		\| 407.82
	\|E		\| E
	\|Major third		\| Major third
	\|-		\|-
	\| -3		\| −3
	\|905.87		\| 905.87
	\|A		\| A
	\|Major sixth		\| Major sixth
	\|-		\|-
	\| -2		\| −2
	\|203.91		\| 203.91
	\|D		\| D
	\|Major second		\| Major second
	\|-		\|-
	\| -1		\| −1
	\|701.96		\| 701.96
	\|G		\| G
	\|Perfect fifth		\| Perfect fifth
	\|-		\|-
	\|'''0'''		\| '''0'''
	\|'''0'''		\| '''0'''
	\|'''C'''		\| '''C'''
	\|Perfect unison / Perfect octave		\| Perfect unison / Perfect octave
	\|-		\|-
	\|1		\| 1
	\|498.05		\| 498.05
	\|F		\| F
	\|Perfect fourth		\| Perfect fourth
	\|-		\|-
	\|2		\| 2
	\|996.09		\| 996.09
	\|Bb		\| Bb
	\|Minor seventh		\| Minor seventh
	\|-		\|-
	\|3		\| 3
	\|294.14		\| 294.14
	\|Eb		\| Eb
	\|Minor third		\| Minor third
	\|-		\|-
	\|4		\| 4
	\|792.18		\| 792.18
	\|Ab		\| Ab
	\|Minor sixth		\| Minor sixth
	\|-		\|-
	\|5		\| 5
	\|90.22		\| 90.22
	\|Db		\| Db
	\|Minor second		\| Minor second
	\|-		\|-
	\|6		\| 6
	\|588.27		\| 588.27
	\|Gb		\| Gb
	\|Diminished fifth		\| Diminished fifth
	\|-		\|-
	\|7		\| 7
	\|1,086.32		\| 1,086.32
	\|Cb		\| Cb
	\|Diminished octave		\| Diminished octave
	\|}		\|}

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	=== Mavila ===		=== Mavila ===
	[[Mavila]] is an exotemperament that flattens the fifth beyond the diatonic range (to around ~~670-680 cents~~) so that the "major third" is flatter than the "minor third", meaning that the "minor third" can be assigned to 5/4 and the "major third" can be assigned to 6/5. This has the effect of "swapping" major and minor intervals from what they are in meantone. This means that the normal chain-of-fifths interval names stop making much sense (but see in [[Mavila#Notation]]).		[[Mavila]] is an exotemperament that flattens the fifth beyond the diatonic range (to around 670–680{{c}}) so that the "major third" is flatter than the "minor third", meaning that the "minor third" can be assigned to 5/4 and the "major third" can be assigned to 6/5. This has the effect of "swapping" major and minor intervals from what they are in meantone. This means that the normal chain-of-fifths interval names stop making much sense (but see in [[Mavila#Notation]]).

	=== Deeptone ===		=== Deeptone ===
	[[Deeptone]] flattens the fifth to around 690 ~~cents~~, so the major third is a [[16/13]] and the augmented third is [[5/4]].		[[Deeptone]] flattens the fifth to around 690{{c}}, so the major third is a [[16/13]] and the augmented third is [[5/4]].

	=== Meantone ===		=== Meantone ===
	[[Meantone]] can be seen as the most "basic" monocot temperament, which flattens the fifth slightly to around 696 ~~cents~~ so that the major third is [[5/4]]. Consequently, the minor third becomes [[6/5]], and the major sixth becomes [[5/3]].		[[Meantone]] can be seen as the most "basic" monocot temperament, which flattens the fifth slightly to around 696{{c}} so that the major third is [[5/4]]. Consequently, the minor third becomes [[6/5]], and the major sixth becomes [[5/3]].

	In the 7-limit, the augmented sixth becomes 7/4, resulting in [[septimal meantone]]. Alternately, the fifth can be flattened further (to around 693 ~~cents~~) so that the diminished seventh is sharper than the augmented sixth. Then, it makes sense to interpret the diminished seventh as 7/4, resulting in [[flattone]] temperament.		In the 7-limit, the augmented sixth becomes 7/4, resulting in [[septimal meantone]]. Alternately, the fifth can be flattened further (to around 693{{c}}) so that the diminished seventh is sharper than the augmented sixth. Then, it makes sense to interpret the diminished seventh as 7/4, resulting in [[flattone]] temperament.

	=== Schismic ===		=== Schismic ===
	[[Schismic]] interprets the diminished fourth, an interval of about 384 ~~cents~~ when justly tuned, as [[5/4]]. This makes it a very accurate microtemperament, and it naturally extends to prime 19 by finding 19/16 at the minor third (called [[nestoria]]).		[[Schismic]] interprets the diminished fourth, an interval of about 384{{c}} when justly tuned, as [[5/4]]. This makes it a very accurate microtemperament, and it naturally extends to prime 19 by finding 19/16 at the minor third (called [[nestoria]]).

	In the 7-limit, the doubly-diminished octave, an interval of about 973 ~~cents~~ when justly tuned, can be interpreted as [[7/4]] with a small loss of accuracy compared to 5-limit schismic; this is called [[garibaldi]].		In the 7-limit, the doubly-diminished octave, an interval of about 973{{c}} when justly tuned, can be interpreted as [[7/4]] with a small loss of accuracy compared to 5-limit schismic; this is called [[garibaldi]].

	=== Superpyth ===		=== Superpyth ===
	[[Superpyth]] interprets the minor seventh as [[7/4]], which suggests a tuning of the perfect fifth at around 710 ~~cents~~. [[5/4]] can then be seen as the augmented second (for standard superpyth) or the double-augmented unison (for [[ultrapyth]], which also extends to prime 13 by setting the major third equal to [[13/10]]).		[[Superpyth]] interprets the minor seventh as [[7/4]], which suggests a tuning of the perfect fifth at around 710{{c}}. [[5/4]] can then be seen as the augmented second (for standard superpyth) or the double-augmented unison (for [[ultrapyth]], which also extends to prime 13 by setting the major third equal to [[13/10]]).

	=== Trienstonian ===		=== Trienstonian ===

Lériendil: /* Temperament interpretations */

2025-09-08T18:34:24Z

Temperament interpretations

← Older revision		Revision as of 18:34, 8 September 2025
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	=== Trienstonian ===		=== Trienstonian ===
	T[[Trienstonian~~\|rienstonian~~]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.		[[Trienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.

	{{Todo\| unify precision }}		{{Todo\| unify precision }}

VectorGraphics at 00:16, 2 September 2025

2025-09-02T00:16:30Z

← Older revision		Revision as of 00:16, 2 September 2025
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	{{Breadcrumb}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=1\|Pergen=[P8, P5]\|Forms=5, 7, 12\|Title=Monocot}}'''Monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth, and the period is a [[2/1]] octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale ([[5L 2s]]) and one of its chromatic children ([[5L 7s]] or [[7L 5s]]) (though there are exotempered exceptions such as [[mavila]] ([[2L 5s]]) and [[trienstonian]] ([[5L 3s]])) and as such they are very commonly used and are a well-explored category of temperaments.

	'''Monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth, and the period is a [[2/1]] octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale ([[5L 2s]]) and one of its chromatic children ([[5L 7s]] or [[7L 5s]]) (though there are exotempered exceptions such as [[mavila]] ([[2L 5s]]) and [[trienstonian]] ([[5L 3s]])) and as such they are very commonly used and are a well-explored category of temperaments.

	== Intervals and notation ==		== Intervals and notation ==

FloraC: Todo

2025-09-01T09:31:50Z

Todo

← Older revision		Revision as of 09:31, 1 September 2025
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	=== Trienstonian ===		=== Trienstonian ===
	T[[Trienstonian\|rienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.		T[[Trienstonian\|rienstonian]] is an exotemperament where the fifth is sharpened so that the major sixth is [[7/4]]. This is thus tuned best with tunings around or sharp of [[5edo]], which do not generate a (usable) diatonic scale.

			{{Todo\| unify precision }}

VectorGraphics at 10:37, 30 August 2025

2025-08-30T10:37:11Z

← Older revision		Revision as of 10:37, 30 August 2025
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			{{Breadcrumb}}

	'''Monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth, and the period is a [[2/1]] octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale ([[5L 2s]]) and one of its chromatic children ([[5L 7s]] or [[7L 5s]]) (though there are exotempered exceptions such as [[mavila]] ([[2L 5s]]) and [[trienstonian]] ([[5L 3s]])) and as such they are very commonly used and are a well-explored category of temperaments.		'''Monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth, and the period is a [[2/1]] octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale ([[5L 2s]]) and one of its chromatic children ([[5L 7s]] or [[7L 5s]]) (though there are exotempered exceptions such as [[mavila]] ([[2L 5s]]) and [[trienstonian]] ([[5L 3s]])) and as such they are very commonly used and are a well-explored category of temperaments.

VectorGraphics: VectorGraphics moved page User:VectorGraphics/Monocot to Ploidacot/Monocot

2025-08-30T10:36:58Z

VectorGraphics moved page User:VectorGraphics/Monocot to Ploidacot/Monocot

← Older revision	Revision as of 10:36, 30 August 2025
(No difference)